Homological tree-based strategies for image analysis

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2={0,1}) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and representative cycles, higher (co)homology operations, etc. This algebraic map φ is described in combinatorial terms using a mixed three-level forest. Different strategies changing only two parameters of this algorithm for computing φ are presented. Each one of those strategies gives rise to different maps, although all of them provides the same homological information for K. For example, tree-based structures useful in image analysis like topological skeletons and pyramids can be obtained as subgraphs of this forest

"Pay Now, Argue Later" Rule – Before and After the Tax Administration Act

The South African Revenue Service (SARS) is entrusted with the duty of collecting tax on behalf of the South African government. In order to ensure effective and prompt collection of taxes, the payment of tax is not suspended pending an objection or an appeal, unless directed otherwise. This is also known as the "pay now, argue later" rule, and, for value-added tax purposes, is provided for in terms of section 36 of the Value-Added Tax Act 89 of 1991. The "pay now, argue later" rule in terms of section 36 of the Value-Added Tax Act prima facie infringes on a taxpayer's right of access to the courts as envisaged in section 34 of the Constitution. This is due to the fact that a taxpayer is obliged to pay tax before being afforded the opportunity to challenge the assessment in a court. In Metcash Trading Ltd v Commissioner for the South African Revenue Service, the Constitutional Court held the "pay now, argue later" rule in terms of section 36 to be constitutional. Olivier, however, does not agree with the court on several matters. Amongst the problems she indicates are that the taxpayer does not have access to the courts at the time the rule is invoked, and that the court did not consider the fact that there might be less invasive means available which would ensure that SARS's duty is balanced with the taxpayer's right of access to the courts. Guidelines were also issued which provide legal certainty regarding the factors SARS may consider in determining whether the payment of tax should be suspended or not. These guidelines also evoked some points of criticism. Since 1 October 2012, the "pay now, argue later" rule has been applied in terms of section 164 of the Tax Administration Act 28 of 2011. The question arises whether this provision addresses the problems identified in respect of section 36 of the Value-Added Tax Act and the guidelines. In comparing these sections, only slight differences emerged. The most significant difference is that section 164(6) of the Tax Administration Act stipulates that the enforcement of tax be suspended for a period when SARS is considering a request for suspension. Section 164(6) does not provide a solution to the problems identified regarding section 36 of the Value-Added Tax Act. It is even possible that this section could give rise to further problems. Therefore, the legislature has failed to address the imbalance between the duties of SARS and the right of a taxpayer to access the courts.   

Connectivity forests for homological analysis of digital volumes

In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of “tunnels” and “holes”, classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs

Genetic variation in Wnt/β-catenin and ER signalling pathways in female and male elite dancers and its associations with low bone mineral density: a cross-section and longitudinal study.

The association of genetic polymorphisms with low bone mineral density in elite athletes have not been considered previously. The present study found that bone mass phenotypes in elite and pre-elite dancers are related to genetic variants at the Wnt/β-catenin and ER pathways. Some athletes (e.g. gymnasts, dancers, swimmers) are at increased risk for low bone mineral density (BMD) which, if untreated, can lead to osteoporosis. To investigate the association of genetic polymorphisms in the oestrogen receptor (ER) and the Wnt/β-catenin signalling pathways with low BMD in elite and pre-elite dancers (impact sport athletes). The study included three phases: (1) 151 elite and pre-elite dancers were screened for the presence of low BMD and traditional osteoporosis risk factors (low body weight, menstrual disturbances, low energy availability); (2) a genetic association study was conducted in 151 elite and pre-elite dancers and age- and sex- controls; (3) serum sclerostin was measured in 101 pre-elite dancers and age- and sex-matched controls within a 3-year period. Eighty dancers revealed low BMD: 56.3% had at least one traditional osteoporosis risk factor, whereas 28.6% did not display any risk factor (37.2% revealed traditional osteoporosis risk factors, but had normal BMD). Body weight, menstrual disturbances and energy availability did not fully predict bone mass acquisition. Instead, genetic polymorphisms in the ER and Wnt/β-catenin pathways were found to be risk factors for low BMD in elite dancers. Sclerostin was significantly increased in dancers compared to controls during the 3-year follow-up (p < 0.05)

Characterization of the association between 8q24 and colon cancer: gene-environment exploration and meta-analysis

<p>Abstract</p> <p>Background</p> <p>Genome-wide association studies and subsequent replication studies have shown that single nucleotide polymorphisms (SNPs) in the chromosomal region 8q24 are associated with colorectal cancer susceptibility.</p> <p>Methods</p> <p>We examined 11 SNP markers in the 8q24 region between 128.47 and 128.54 Mb, using a total of 1,987 colon cases and 2,339 controls who self-reported as white from two independent, well-characterized study populations. Analysis was performed separately within each study, and combined using random effects meta-analysis. Logistic regression was used to estimate odds ratios (ORs) and 95% confidence intervals (95% CIs) and to test for effect modification by known colon cancer risk factors. We also performed a meta-analysis combining our results with previous studies.</p> <p>Results</p> <p>We observed evidence of association for four SNPs in low to high linkage disequilibrium (r²ranging from 0.18 to 0.93) localized in a 16.2 kb region defined by rs10505477 and rs1056368. The combined results for our two studies of colon cancer showed an OR of 1.10 (95% CI: 1.01-1.20, P_trend= 0.023), and a meta-analysis of our results with previously reported studies of colon and colorectal cancer strongly support the association for this SNP (combined OR for rs6983267 = 1.21, 95% CI: 1.18-1.24, p = 5.5 × 10^-44). We did not observe any notable evidence of effect modification by known colon cancer risk factors, and risk did not differ significantly by tumor site or stage.</p> <p>Conclusions</p> <p>Our study confirms the association between polymorphisms on chromosome 8q24 and colon cancer risk and suggests that the susceptibility locus in region 8q24 is not strongly modified by various lifestyle, environmental, and demographic risk factors for colon cancer.</p

Homological computations in electromagnetic modeling

The users of modern design software for electrical appliances can accidentally attempt an analysis of ill-posed design problems, ones with no sensible solution. It is tedious to track down such mistakes manually, but certain topological objects, the homology groups, provide systematic procedures for detection of such mistakes. However, the procedures are not necessarily practical if the time consumed in computation of the homology groups is excessive. This thesis analyzes the electromagnetic modeling problems and different methods to compute homology groups for the models. A strong emphasis is placed on the computational complexity. The spatial model for electromagnetics, differentiable manifold with boundary, is introduced and some machinery is constructed to define its integer-coefficient homology groups. Their computation is expressed in terms of standard computational problems of Abelian group theory. The problems involve integer matrix computations, where large intermediate results may emerge and require attention in complexity analysis. The problems admit polynomial-time solution, but some of the polynomials are of unacceptably high degree. Particularly, the computation is known to consume considerable time if the homology groups have torsion subgroups, and this possibility in electromagnetic models is investigated in detail. Also, homologies over different coefficient groups are introduced as alternatives and their connection with integer-coefficient homology is characterized. Numerical computation typically requires tessellations of electromagnetic models into elements --- up to millions, even if the model is homologically rather simple. This is an unnecessary burden for the group theoretic solution schemes, and various methods are introduced to simplify the tessellations into a modest fraction of the original and thus reduce the overall computational complexity. Unfortunately, the methods do not admit rigorous performance bounds, but remain heuristics, leaving the rigorous upper bound for overall complexity very pessimistic: the overall time hardly ever attains the bound in any practical design problem

Homological computations in electromagnetic modeling

The users of modern design software for electrical appliances can accidentally attempt an analysis of ill-posed design problems, ones with no sensible solution. It is tedious to track down such mistakes manually, but certain topological objects, the homology groups, provide systematic procedures for detection of such mistakes. However, the procedures are not necessarily practical if the time consumed in computation of the homology groups is excessive. This thesis analyzes the electromagnetic modeling problems and different methods to compute homology groups for the models. A strong emphasis is placed on the computational complexity. The spatial model for electromagnetics, differentiable manifold with boundary, is introduced and some machinery is constructed to define its integer-coefficient homology groups. Their computation is expressed in terms of standard computational problems of Abelian group theory. The problems involve integer matrix computations, where large intermediate results may emerge and require attention in complexity analysis. The problems admit polynomial-time solution, but some of the polynomials are of unacceptably high degree. Particularly, the computation is known to consume considerable time if the homology groups have torsion subgroups, and this possibility in electromagnetic models is investigated in detail. Also, homologies over different coefficient groups are introduced as alternatives and their connection with integer-coefficient homology is characterized. Numerical computation typically requires tessellations of electromagnetic models into elements --- up to millions, even if the model is homologically rather simple. This is an unnecessary burden for the group theoretic solution schemes, and various methods are introduced to simplify the tessellations into a modest fraction of the original and thus reduce the overall computational complexity. Unfortunately, the methods do not admit rigorous performance bounds, but remain heuristics, leaving the rigorous upper bound for overall complexity very pessimistic: the overall time hardly ever attains the bound in any practical design problem

Geometric T-Omega approach to solve eddy-currents coupled to electric circuits

This paper describes a systematic geometric approach to solve magneto-quasi-static coupled field\u2013circuit problems. The field problem analysis is based on formulating the boundary value problem with an electric vector potential and a scalar magnetic potential. The field\u2013circuit coupling and the definition of potentials are formally examined within the framework of homology theory